Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t Subscript alpha divided by tα/2​, ​(b) find the critical value z Subscript alpha divided by zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn​ girls: n= 177, overbarx= 32.7 ​hg, s = 6.2 hg. The confidence level is 99​%.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A) ta/2 = _

B) Za/2 = _

C) Neither the normal distribution nor the t distribution applies.

Answer 1

Solution :

Given that,

= 32.7

s = 6.2

n =177

Degrees of freedom = df = n - 1 = 177 - 1 = 176

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,176 =2.604

Margin of error = E = t/2,df * (s /n)

= 2.604 * (6.2/ 177)

= 1.21

Margin of error = 0.50

The 99% confidence interval estimate of the population mean is,

- E < < + E

32.7 - 1.21 < < 32.7 + 1.21

31.49 < < 33.91

(31.49, 33.91 )